Atlus has completely remodeled the structure of the game's files, and changed the game from 32-bit to 64-bit, so existing mods no longer work. I was going to redo my mod after I could find some new tools to do it, but I found that somebody already made a better solution on the new mod tools, so I'm just going to give you a simplified guide on how to get that working below. The upside is that this solution doesn't break the cutscene viewer, and will also allow you to easily add other mods in the future with little effort.

I'll leave my old mod guide up for now for the people who are sticking with the old 32-bit version of the game for one reason or another.

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The process of modifying the game files is a bit convoluted and making a full guide for that will take a while. For now I'm gonna first release an automated patch that will just create a modified game file for you, and then later I'll make the full walkthrough of how I made the modification later.

Update (Sep 4, 2020): Patch has been updated for latest version of game.

Unfortunately, the updated patch removes the new intro even in the Big TV menu, as attempts to swap the new intro into the old intro's slot in the files just causes the game to crash currently. Most likely a direct mod of the game would be needed to get a better result, and I don't have the skills for that.

The new mod is courtesy of Pixelguin over @ GameBanana
The below is a simplified guide to get it working, since existing documentation is kinda messy at the moment.

1. Install Reloaded II mod manager by downloading and running the latest Setup.exe from its GitHub Page[github.com].
   
2. Launch Reloaded II if it didn't automatically launch, There should be a shortcut on your Desktop.
   
3. Follow the tutorial to add P4G.exe to the manager, it'll be in "C:\Program Files (x86)\Steam\steamapps\common\Day\P4G.exe" unless you moved your Steam Library to a different location.
   
4. Next, Copy the below URL (DON'T CLICK) and paste it into your browser. If your browser asks if you want to launch the program, say yes. Reloaded II should automatically install the mod.
   
   r2:https://gamebanana.com/mmdl/923048

   Alternatively: Go to the "Download Mods" top-left section in Reloaded II and search "P4 Opening Movie" to find and download the mod.

5. Next in Reloaded II, select the P4G logo on the left, and then click "Launch Application". The manager should install a few more needed mods automatically before launching the game, then you should now see the classic P4 Intro video play.
   
6. Finally, ALT+F4/Exit the game, go to your Desktop, right-click the Reloaded II shortcut and open its Properties. Copy the "Target:" path to its EXE file.
   
7. Go back to Steam, right-click on P4G and go to its Properties. Under "Launch Options" paste the Reloaded II path followed by "--launch %command%" so it should look something like this:
   
   C:\Users\username\Desktop\Reloaded-II\Reloaded-II.exe --launch %command%

Close the Properties and you're done. Now when you launch P4G from Steam it should auto-load the mod and launch the game. Plus, you can now go into the Cutscene viewer and play both Intro videos like normal, unlike my old mod.

This is an automated patch which will do all the hardwork for you. The original files will be backed up in the process, but in the worst-case scenario you can just use Steam's "Verify integrity of Game Files..." tool to redownload the original files and fix your game that way.

What this patch does is swap the old intro with the new intro. So the launch intro will be the old intro, and if you pull up the Ch4 Big TV video viewer in the TV Listing the intros will be swapped there as well. Updated patch removes the new intro from Big TV as well due to technical issues.

1. Download the patch here:
   https://drive.google.com/file/d/1xWC46lUBzIk_HVI9eZpPCojLEvyXloFA/view?usp=sharing
2. Extract the contents of the downloaded ZIP file into an empty folder
   
3. Now right-click on the game in Steam and go to 'Manage -> Browse local files'
   
4. Copy the game file
   movie00002.pac
   into the patch folder
   
5. Open the
   movie00002 Patch.bat
   file.
   
6. Follow the directions in the window that appears. If you see any errors, screenshot the window and close it, don't continue. Post the error in the comments.
   
7. After following the directions in the window, it should close and automatically remove the patch files leaving just the modified
   movie00002.pac
   file and the backed up original.
   
8. Copy the modified
   movie00002.pac
   file into your game directory and overwrite the existing file.

Now launch your game and enjoy!